Crossed products of Hilbert $C*$-modules
HTML articles powered by AMS MathViewer
- by Huu Hung Bui PDF
- Proc. Amer. Math. Soc. 125 (1997), 1341-1348 Request permission
Abstract:
We define the notion of crossed products of Hilbert $C^*$-modules by regular multiplicative unitaries, which is a generalization of the notion of crossed products of $C^*$-algebras. Crossed products of Hilbert $C^*$-modules arise naturally as imprimitivity bimodules for the crossed products of Morita equivalent $C^*$-algebras.References
- Bruce Blackadar, $K$-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986. MR 859867, DOI 10.1007/978-1-4613-9572-0
- Huu Hung Bui, Morita equivalence of twisted crossed products by coactions, J. Funct. Anal. 123 (1994), no. 1, 59–98. MR 1279296, DOI 10.1006/jfan.1994.1083
- Huu Hung Bui, Full coactions on Hilbert $C^*$-modules, J. Austral. Math. Soc. Ser. A 59 (1995), no. 3, 409–420. MR 1355231
- Saad Baaj and Georges Skandalis, $C^\ast$-algèbres de Hopf et théorie de Kasparov équivariante, $K$-Theory 2 (1989), no. 6, 683–721 (French, with English summary). MR 1010978, DOI 10.1007/BF00538428
- Saad Baaj and Georges Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de $C^*$-algèbres, Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 4, 425–488 (French, with English summary). MR 1235438
- Robert S. Doran and Josef Wichmann, Approximate identities and factorization in Banach modules, Lecture Notes in Mathematics, vol. 768, Springer-Verlag, Berlin-New York, 1979. MR 555240
- S. Echterhoff and I. Raeburn, Multipliers of imprimitivity bimodules and Morita equivalence of crossed products, Math. Scand., 76(1995), 289-309.
- E. C. Lance, Hilbert $C^*$-modules, London Mathematical Society Lecture Note Series, vol. 210, Cambridge University Press, Cambridge, 1995. A toolkit for operator algebraists. MR 1325694, DOI 10.1017/CBO9780511526206
- M. B. Landstad, J. Phillips, I. Raeburn, and C. E. Sutherland, Representations of crossed products by coactions and principal bundles, Trans. Amer. Math. Soc. 299 (1987), no. 2, 747–784. MR 869232, DOI 10.1090/S0002-9947-1987-0869232-0
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
- S. L. Woronowicz, Unbounded elements affiliated with $C^*$-algebras and noncompact quantum groups, Comm. Math. Phys. 136 (1991), no. 2, 399–432. MR 1096123
Additional Information
- Huu Hung Bui
- Affiliation: School of Mathematics, Physics, Computing and Electronics, Macquarie University, New South Wales 2109, Australia
- Address at time of publication: School of Mathematics, University of New South Wales, Sydney 2052, New South Wales, Australia
- Email: hung@macadam.mpce.mq.edu.au, hung@alpha.maths.unsw.edu.au
- Received by editor(s): August 4, 1995
- Received by editor(s) in revised form: October 6, 1995, October 12, 1995, and October 30, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1341-1348
- MSC (1991): Primary 46L05, 22D25
- DOI: https://doi.org/10.1090/S0002-9939-97-03656-3
- MathSciNet review: 1363451